Well the algo is quite simple, let's try to break it down:
if (code.Substring(0, 2) != "DC")
It has to start with DC
if (code.Length != 0x1a)
and be of length 26 chars
string s = code.Substring(2, 14);
byte[] buffer1 = new SHA256Managed().ComputeHash(Encoding.UTF8.GetBytes(s));
then take the 14 chars starting from third (skip DC) and calculate SHA256 on it.
After that the checks are (extracted)
string str2 = ConvertToB36(Convert.ToInt32(buffer1[13])).PadLeft(2, '0');
code.Substring(0x10, 2) == str2
so value on 13 index of SHA has to be equal (converted to BASE36) to 2 chars from the input starting from pos 16.
The rest of the checks are similar.
So your keygen would consist only the functions that you already has in the code.
So the general key is in this form (psudocode)
input = ""
sha = SHA256(input)
print "DC"+input+sha[13].encode('base36')+sha[10].encode('base36')+sha[5].encode('base36')+sha[17].encode('base36')+sha[25].encode('base36')